[1 + c(LIF)^-1(g0i/g00)(dx^i/dt) + c(LIF)^-2gij(dx^i/dt)(dx^j/dt)]^-1/2ds(invariant) = c(LIF)dT(LNIF)

GAMMA(LNIF)ds(LNIF) = GAMMA(LNIF')ds(LNIF')

f(LNIF')GAMMA(LNIF) = f(LNIF)GAMMA(LNIF')

f(LNIF')/f(LNIF) = GAMMA(LNIF')/GAMMA(LNIF)

also

f(LNIF')/f(LIF) = GAMMA(LNIF')

because GAMMA(LIF) = 1

note all of these frames are LOCALLY COINCIDENT  

also under certain conditions the LIF can be approximately equivalent to a static LNIF far away from the source.

GAMMA = [1 + c(LIF)^-1(g0i/g00)(dx^i/dt) + c(LIF)^-2gij(dx^i/dt)(dx^j/dt)]^-1/2

= [1 + c(LIF)^-1A.v/g00 + c(LIF)^-2gij(dx^i/dt)(dx^j/dt)]^-1/2